Question

Find the principal value $cot^{-1} (1)$

• A. $\frac{\pi}{3}$
• B. $\frac{\pi}{4}$
• C. $\frac{\pi}{2}$
• D. $0$

Answer 1

Answer: (B)

Let $cot^{-1} \left(1\right) = \theta $
$\Rightarrow \,cot\,\theta = 1$
$= cot \frac{\pi}{4}$
$\Rightarrow \,\theta = \frac{\pi}{4} \in (0$, $\pi)$
$\therefore $ Principal value of $cot^{-1} \left(1\right)$ is $\frac{\pi }{4}$